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2 years ago

12

Jack puts 2 photos on each of 7 pages of his photo album. How many photos does he use? Complete the jumps on the number lineby a

dding arrows.

1 answer:

Ray Of Light [21]2 years ago

4 0

Answer:

Jack uses 14 photos.

Step-by-step explanation:

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A rectangle has an area of 45x2 − 42x − 48 and a width of 5x − 8. What is the length of the rectangle?

Irina18 [472]

Dividend

Divisor

and

9x+6

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2 years ago

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Here are seven tiles: 1,1,3,3,3,5,5. Tom takes a tile at random. He does not replace the tile. Tom then takes a second tile. A)

zzz [600]

Answer:

a) 2/42

b)16/42

Step-by-step explanation:

a) 2/7 x 1/6 = 2/42

b) (1,2) (1,3) (2,3)

P(1,2) = 2/7 x 3/6 = 6/42

P(1,3) = 2/7 x 2/6 = 4/42

P(2,3) = 3/7 x 2/6 = 6/42

Add all = 6/42 + 4/42 + 6/42 = 16/42

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2 years ago

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

Step-by-step explanation:

Part 1)

The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:

$\displaystyle L \approx f'(a)(x-a) + f(a)$

We want to verify that the expression:

$1-36x$

Is the linear approximation for the function:

$\displaystyle f(x) = \frac{1}{(1+9x)^4}$

At <em>x</em> = 0.

So, find f'(x). We can use the chain rule:

$\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)$

Simplify. Hence:

$\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}$

Then the slope of the linear approximation at <em>x</em> = 0 will be:

$\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36$

And the value of the function at <em>x</em> = 0 is:

$\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1$

Thus, the linear approximation will be:

$\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x$

Hence verified.

Part B)

We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.

In other words:

$\displaystyle \left| f(x) - L(x) \right | \leq 0.1$

By definition:

$\displaystyle -0.1\leq f(x) - L(x) \leq 0.1$

Therefore:

$\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1$

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

4 0

2 years ago

Angelique had 20 tokens to use for games at the arcade. She lost some of them. Her dad tripled the tokens she had left. Angeliqu

alexandr402 [8]

Answer: Both the expressions are exactly same . Both are representing the number of tokens she has now.

Step-by-step explanation:

Given: The total number of tokens Angelique has= 20

Since, she lost some of them, let the number of lost tokens be t.

Then, The remaining tokens she has = 20-t

Then her father triples the tokens she has.

now, the number of token she has= $3(20-t)$ ....>Angelique's expression

By using distributive property,

The number of token she has= $3\times20-3t$

⇒The number of token she has= $60-3t$ ...> Dante's expressions

Hence, both are the same expressions. Both are representing the number of tokens she has now.

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2 years ago

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A food packet is dropped from a helicopter and is modeled by the function f(x) = -16x2 + 14400. The graph below shows the height

Elis [28]

From the graph, the domain is 0 ≤ x ≤ 30

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2 years ago

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